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Simplifying 9x2 + 18x + 7 = 9x2 + (9x2 + -18x + 9) Reorder the terms: 7 + 18x + 9x2 = 9x2 + (9x2 + -18x + 9) Reorder the terms: 7 + 18x + 9x2 = 9x2 + (9 + -18x + 9x2) Remove parenthesis around (9 + -18x + 9x2) 7 + 18x + 9x2 = 9x2 + 9 + -18x + 9x2 Reorder the terms: 7 + 18x + 9x2 = 9 + -18x + 9x2 + 9x2 Combine like terms: 9x2 + 9x2 = 18x2 7 + 18x + 9x2 = 9 + -18x + 18x2 Solving 7 + 18x + 9x2 = 9 + -18x + 18x2 Solving for variable 'x'. Reorder the terms: 7 + -9 + 18x + 18x + 9x2 + -18x2 = 9 + -18x + 18x2 + -9 + 18x + -18x2 Combine like terms: 7 + -9 = -2 -2 + 18x + 18x + 9x2 + -18x2 = 9 + -18x + 18x2 + -9 + 18x + -18x2 Combine like terms: 18x + 18x = 36x -2 + 36x + 9x2 + -18x2 = 9 + -18x + 18x2 + -9 + 18x + -18x2 Combine like terms: 9x2 + -18x2 = -9x2 -2 + 36x + -9x2 = 9 + -18x + 18x2 + -9 + 18x + -18x2 Reorder the terms: -2 + 36x + -9x2 = 9 + -9 + -18x + 18x + 18x2 + -18x2 Combine like terms: 9 + -9 = 0 -2 + 36x + -9x2 = 0 + -18x + 18x + 18x2 + -18x2 -2 + 36x + -9x2 = -18x + 18x + 18x2 + -18x2 Combine like terms: -18x + 18x = 0 -2 + 36x + -9x2 = 0 + 18x2 + -18x2 -2 + 36x + -9x2 = 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 -2 + 36x + -9x2 = 0 Begin completing the square. Divide all terms by -9 the coefficient of the squared term: Divide each side by '-9'. 0.2222222222 + -4x + x2 = 0 Move the constant term to the right: Add '-0.2222222222' to each side of the equation. 0.2222222222 + -4x + -0.2222222222 + x2 = 0 + -0.2222222222 Reorder the terms: 0.2222222222 + -0.2222222222 + -4x + x2 = 0 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + -4x + x2 = 0 + -0.2222222222 -4x + x2 = 0 + -0.2222222222 Combine like terms: 0 + -0.2222222222 = -0.2222222222 -4x + x2 = -0.2222222222 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -0.2222222222 + 4 Reorder the terms: 4 + -4x + x2 = -0.2222222222 + 4 Combine like terms: -0.2222222222 + 4 = 3.7777777778 4 + -4x + x2 = 3.7777777778 Factor a perfect square on the left side: (x + -2)(x + -2) = 3.7777777778 Calculate the square root of the right side: 1.943650632 Break this problem into two subproblems by setting (x + -2) equal to 1.943650632 and -1.943650632.Subproblem 1
x + -2 = 1.943650632 Simplifying x + -2 = 1.943650632 Reorder the terms: -2 + x = 1.943650632 Solving -2 + x = 1.943650632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.943650632 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.943650632 + 2 x = 1.943650632 + 2 Combine like terms: 1.943650632 + 2 = 3.943650632 x = 3.943650632 Simplifying x = 3.943650632Subproblem 2
x + -2 = -1.943650632 Simplifying x + -2 = -1.943650632 Reorder the terms: -2 + x = -1.943650632 Solving -2 + x = -1.943650632 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.943650632 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.943650632 + 2 x = -1.943650632 + 2 Combine like terms: -1.943650632 + 2 = 0.056349368 x = 0.056349368 Simplifying x = 0.056349368Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.943650632, 0.056349368}
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